相关论文: Non-equilibrium scaling limit for a tagged particl…
We prove a Functional Central Limit Theorem for the position of a Tagged Particle in the one-dimensional Asymmetric Simple Exclusion Process in the hyperbolic scaling, starting from a Bernoulli product measure conditioned to have a particle…
Many physical systems share the property of scale invariance. Most of them show ordinary power-law scaling, where quantities can be expressed as a leading power law times a scaling function which depends on scaling-invariant ratios of the…
In this paper we consider three classes of interacting particle systems on $\mathbb Z$: independent random walks, the exclusion process, and the inclusion process. We allow particles to switch their jump rate (the rate identifies the type…
We consider the stochastic ranking process with space-time dependent unbounded jump rates for the particles. We prove that the joint empirical distribution of jump rate and scaled position converges almost surely to a deterministic…
We consider a particle system with weights and the scaling limits derived from its occupation time. We let the particles perform independent recurrent L\'evy motions and we assume that their initial positions and weights are given by a…
Anomalous coarsening in far-from equilibrium one-dimensional systems is investigated by simulation and analytic techniques. The minimal hard core particle (exclusion) models contain mechanisms of aggregated particle diffusion, with rates…
In this article we obtain the equilibrium fluctuations of a symmetric exclusion process in $\mathbb{Z}$ with long jumps. The transition probability of the jump from $x$ to $y$ is proportional to $|x-y|^{-\gamma-1}$. Here we restrict to the…
Continuous time random walks impose a random waiting time before each particle jump. Scaling limits of heavy tailed continuous time random walks are governed by fractional evolution equations. Space-fractional derivatives describe heavy…
The exit problem for small perturbations of a dynamical system in a domain is considered. It is assumed that the unperturbed dynamical system and the domain satisfy the Levinson conditions. We assume that the random perturbation affects the…
We study an interacting particle system in $\mathbf{R}^d$ motivated by Stein variational gradient descent [Q. Liu and D. Wang, NIPS 2016], a deterministic algorithm for sampling from a given probability density with unknown normalization.…
We consider simple exclusion processes on Z for which the underlying random walk has a finite first moment and a non-zero mean and whose initial distributions are product measures with different densities to the left and to the right of the…
The unbounded diffusion observed for the standard mapping in a regime of high nonlinearity is suppressed by dissipation due to the violation of Liouville's theorem. The diffusion coefficient becomes important for the description of scaling…
We compute the growth fluctuations in equilibrium of a wide class of deposition models. These models also serve as general frame to several nearest-neighbor particle jump processes, e.g. the simple exclusion or the zero range process, where…
We study semi-infinite particle systems on the one-dimensional integer lattice, where each particle performs a continuous-time nearest-neighbour random walk, with jump rates intrinsic to each particle, subject to an exclusion interaction…
We establish via a probabilistic approach the quenched invariance principle for a class of long range random walks in independent (but not necessarily identically distributed) balanced random environments, with the transition probability…
In these lectures, we shall present some remarkable results that have been obtained for systems far from equilibrium during the last two decades. We shall put a special emphasis on the concept of large deviation functions that provide us…
Consider the weakly asymmetric simple exclusion processes on the one-dimensional torus. We study the non-equilibrium fluctuation of a class of additive functionals, and show that its scaling limit is a Gaussian process. The proof is mainly…
Recent progress in out-of-equilibrium closed quantum systems has significantly advanced the understanding of mechanisms behind their evolution towards thermalization. Notably, the concept of non-thermal fixed points (NTFPs) - responsible…
We obtain invariance principles for a wide class of fractionally integrated nonlinear processes. The limiting distributions are shown to be fractional Brownian motions. Under very mild conditions, we extend earlier ones on long memory…
Small thermodynamic systems exhibit peculiar behavior different from that observed in long-scale systems. Non-equilibrium processes taking place in those systems are strongly influenced by the presence of fluctuations which can be large.…